Published July 1, 1968
Black Lipid Membranes at Bifaces
Formation characteristics,optical and
some thermodynamic properties
H. TI TIEN
From the Department of Biophysics, Michigan State University, East Lansing, Michigan 48823
Black lipid membranes (BLM) less than 90 A thick have been
shown to be the most realistic approach to biological membrane models. This
paper describes the formation characteristics, optical properties, and thermodynamics of BLM at water/oil/water bifaces. In particular, the nature of the
Plateau-Gibbs border which supports the black membrane is analyzed in some
detail. The formation of BLM at the biface involves a spontaneous reduction
of the free energy of the system. As long as the integrity of the membrane is
maintained, the limiting structure of the BLM represents the lowest free energy
configuration.
ABSTRACT
125 s
The Journal of General Physiology
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Although at present the molecular organization of natural membranes has
not been definitely settled, the general picture of membrane structure, widely
accepted today, is that based upon the bimolecular lipid layer with adsorbed
protein monolayers (for a current review, see reference 1). This model of the
cell membrane rests, in part, on the foundation of the bimolecular lipid
leaflet concept of Gorter and Grendel (2), which was deduced from the
classical monolayer experiments. The postulated adsorbed protein layers had
their origin in experiments initiated by Harvey and Shapiro (3) and by Cole
(4) in the 1930s. Indirect experimental evidence in support of the bimolecular
leaflet model (with adsorbed protein layers) has been provided by numerous
studies such as X-ray diffraction, electron microscopy, permeability, electrical
resistance and capacitance, and chemical analyses (5). Therefore, it has been
evident from earlier years that, if the bimolecular lipid layer were indeed
the major structural component of cellular membranes, knowledge concerning
the properties and the formation of such a structure in vitro would be of
considerable significance, both experimentally and theoretically. It was
readily apparent also that a detailed physical chemical description of natural
membranes would be best approached by studies of simpler, well-defined
models, owing to the great complexity of living systems.
Among the various membrane models investigated, it is generally recog-
Published July 1, 1968
126 s
MODELS
AND MODEL
MEMBRANES
nized that bimolecular lipid membranes (or BLM)5 represent the closest
approach to the problem of natural membrane models (6, 7). A review of the
studies on BLM is available (8). In the present paper, optical and interfacial
properties of BLM at the biface 2 are discussed together with the results of
further investigations summarized in the following paragraphs.
FORMATION
OF
CHARACTERISTICS
BLM
Experimentally, a BLM is formed as follows. A small amount of suitable lipid
solution (see Table I) is introduced onto an opening in the wall of a hydrophobic support (such as Teflon or polyethylene) immersed in an aqueous
TABLE I
Yi
Compound
Remarks
dynes/cm
1.
2.
3.
4.
5.
6.
7.
8.
9.
Hexadecyltrimethylammonium bromide
(HDTAB)*
Dioctadecyl phosphite (DODP)*
Dodecyl acid phosphate (DAP)*
Glycerol distearate (GDS)
Glycerol dioleate (GDO)
Sodium dodecyl sulfate (Na-DS)*
N-Lauryl,myristyl-4-aminopropionic acid
(Deriphat -170C)*
Lecithin (egg)
Oxidized cholesterol
0.15
5.7
1.1
1.5
1.5
0.9
1.9
Dissolved in the aqueous
phase, cationic
Nonionic
Anionic
Nonionic
Nonionic
Anionic
Amphoteric
Amphoteric
?
* Used in combination with freshly recrystallized cholesterol.
solution. The formation characteristics of lipid membranes are quite similar
to those of soap films in air (9). When first formed, the lipid membrane at the
biface is usually thick, and interference colors may not be visible as viewed
through a low-power microscope (10-40X) in reflected white light. Under
suitable conditions, the thick membrane begins to thin spontaneously. When
the membrane is still sufficiently thick (0.1-1 ), the structure of the membrane is pictured as being similar to that of a sandwich consisting of an organic phase between two adsorbed monolayers of lipid molecules at the biface.
At a distance more than 100 A, the attraction of the lipid monolayers across
I Since the thickness does not greatly differ from the length of two lipid molecules used, and owing to
the optically "black" appearance, these membranes are called bimnolecular, bilayer, or black lipid
membranes, abbreviated as BLM.
2 The word "biface" is introduced to describe the two coexisting water/oil or solution/membrane
interfaces.
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COMPOUNDS USED IN BLM FORMATION AND
INTERFACIAL TENSION DATA AT 25°C
Published July 1, 1968
H. T TIEN
Black Lipid Membranes at Bifaces
127 S
the biface is small. The chief cause of thinning therefore takes place because
of the presence of a Plateau-Gibbs border, i.e. the edge where the membrane
is terminated. At the Plateau-Gibbs border, the pressure is less than in the
interior of the thick membrane owing to the concave interfaces. The PlateauGibbs (or P-G) border at the biface therefore exerts a strong suction upon the
interior of the thick membrane, causing a rapid reduction in its thickness.
The rate of thinning prior to the appearance of "black spots" follows that of
Tt 2
constant relation, where T is the time and t is the membrane thickness.
However, the appearance of black spots (bimolecular or multiples of bilayer
thickness) results in a greatly increased rate of thinning. It has been suggested
that a "zipper-like" action, which is apparently also important in producing
changes in a thin membrane, is an additional cause for the rapid growth of
black area. It should be mentioned that the interference colors and black
formation are highly variable using the brush technique. Fig. 1 shows an
atypical picture of BLM during its formation.
Because of very small difference in specific gravity between the lipid solution
and the bathing medium, the lipid membranes formed in the usual manner
(i.e. with vertical orientation) behave essentially like horizontal soap films.
As can be seen in Fig. 1, the boundary between the black and thicker region
is circular instead of a horizontal line. It has been noted by earlier workers
(7) that BLM are most prone to rupture during their formation. This premature demise of BLM may be explained by the fact that the boundary
between the two areas is the seat of high concentration stress and turbulence
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1. The growth of a black (bimolecular) lipid membrane in aqueous solution.
This photograph is reproduced from a frame of a motion picture first shown at the Symposium on the Plasma Membrane held by the New York Heart Association, New York,
December 1961. Magnification about X 50.
FIGURE
Published July 1, 1968
128 s
MODELS
AND MODEL
MEMBRANES
owing to the rapid drainage of the lipid solution. Therefore, the rupture
would most likely occur somewhere along this boundary. It is of some interest
here that the transition from a black area to that of a thicker region does not
appear to be gradual, but rather is very sharply delineated. The reason for
this apparent sharp boundary may be made clear by the following analysis,
which is the explanation used in the case of soap films (9). We may consider
that the black area of a lipid membrane is, to a first approximation, an interface between two aqueous solutions, I and II (Fig. 2). At point N, where
three interfaces meet-thick film/solution I, the interface between the two
°
solutions, and solution II/thick film the angles are set at 120 apart. The
distance B, the transition region from the black to the thicker part of the
membrane, is given by
B=
cot0
(1 )
For a silvery-golden membrane (i.e. before the transition to the black state),
S is about 1000 A. The transition region B is therefore calculated to be only
about 290 A. Hence a very sharp demarcation is to be expected when the
boundary is observed under low magnification.
It should be pointed out that a black or grayish-black lipid membrane may
not necessarily be bimolecular or bilayer in thickness. In fact, we have observed
at least three shades of black for BLM formed from Escherichia coli lipids.
Under appropriate conditions, these BLM can be made to go from one stage
of "blackness" to the next, with a very long time interval between the stages.
However, removal of lipid solution around the membrane or otherwise
disturbing the'thick membrane by mechanical means would generally speed
up the growth of the secondary (limiting) black structure.
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FIGURE 2. The boundary between black area and thick region of the membrane. A
trace of the photograph (Fig. 1) is shown at left. The sharp demarcation between BLM
(-70 A) and colored film ( 1000-6000 A) is illustrated in the enlarged drawing (crosssectional view) at right. S = thickness of the color film; N = intersection of the three
interfaces; B = thickness of the transition region (B = S cot 0/2).
Published July 1, 1968
H. T TIEN
THE PLATEAU-GIBBS
BLM
129
Black Lipid Membranes at Bifaces
BORDER
AND
STABILITY
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There are at least two major problems associated with BLM investigations.
First, we do not know precisely what molecular species are present in the
membrane. The second problem is the fragility of the structure, which presents
considerable experimental difficulties in investigating its mechanical and
other properties. In many ways, therefore, our description of the BLM will
necessarily be qualitative. In our consideration of the relationship between
the BLM and its Plateau-Gibbs border, we shall follow the analysis put forth
by investigators in the field of soap films (10-12). As mentioned earlier, the
edge where the BLM is terminated is called the Plateau-Gibbs border and is
believed to be essential for the integrity of BLM structure. It has been frequently observed that the area of BLM does not usually extend over to the
entire aperture in the membrane support. That means that the BLM may
occupy anywhere from nearly none to almost 100% of the total available area
at the biface. Before offering an explanation of why this is so, let us consider
qualitatively the factors which are likely to be involved in the BLM stability.
During the formation stages of BLM, when a drop of lipid solution is introduced onto the aperture in the membrane support, thereby creating two
coexisting interfaces or a biface, three events are likely to take place: (a) the
lipid solution will thin down spontaneously to give a BLM in equilibrium with
its P-G border or break; (b) the lipid solution will drain sufficiently to give a
colored lipid film but will remain in this state for a long period of time if not
disturbed; (c) the lipid solution will remain as a globule. We shall limit our
consideration to case a. It is evident that the existence of a BLM at the biface
must be due to a balance of forces. At equilibrium the attractive forces must
be equal to repulsive forces. In terms of the free energy F of the system,
dF/dt = 0, where t is the thickness of BLM. The attractive forces most likely
would include van der Waals' attraction and P-G border suction, whereas the
counterforces consist of Born repulsion and electric double layers situated at
the biface. The Born repulsion or steric effect arises at a very short distance
(at the bimolecular length of the lipid used) and increases rapidly when the
limiting thickness of BLM is passed. At equilibrium, Born repulsion is perhaps
much more important than the double-layer repulsion in counteracting the
van der Waals forces and P-G border pressure. As has been mentioned earlier,
a number of "black" states are possible for BLM. This means that in the free
energy vs. BLM thickness plot a number of minima are present, corresponding
to each "black" state. If the final black state (secondary black) represents the
limiting structure of the BLM consisting of a bimolecular leaflet of lipid
molecules, the other black states must be multiples of this basic unit. Although
Published July 1, 1968
130 s
MODELS
AND MODEL
MEMBRANES
quantitative calculations along these lines are as yet unavailable, the interplay
of these forces must be responsible for the existence of these BLM (8).
In going from the "colored" state to the final "black" state, the excess
lipid solution used usually ends up in the P-G border. A small fraction of it
could either form microlenses adhering to the BLM or dissolve in the ambient
solution. We now attempt an explanation for case a, where a BLM is formed
Y a
N
\
\ R
I
1
U
(A)
(B)
3. The Plateau-Gibbs border and BLM. At the left is shown the front view of a
BLM on a hydrophobic support (outermost circle). The numbers 1 and 2 refer to different
areas occupied by BLM. A cross-sectional view of the P-G border is shown at right. Numerals I, II, and III denote, respectively, aqueous phases I and II, and the lipid solution
phase. N = line of intersection of the three interfaces; y' and y" = interfacial tension of
various interfaces; R = radius of the P-G border. In case yBLM < 2y, the P-G border will
FIGuRE
move toward the edge (shaded). This situation is described by
YBLM
=
2
ML COs 0 (see
the text).
spontaneously but the observable BLM area varies when formed under
different experimental conditions.
In Fig. 3 A, a front view of BLM is shown with different observable areas
labeled 1 and 2. At equilibrium, there are three forces intersecting along a
line of contact (represented by point N), which is shown in a cross-sectional
view in Fig. 3 B. Here BLM separates aqueous phases I and II. The third
liquid phase, designated by III, is the lipid solution in the P-G border. The
law of Neumann's triangle states that, at equilibrium,
YBLM
=
Y--III COS a +
yI--III COS
(2)
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BLM
Published July 1, 1968
I31 S
H. Ti TIEN Black Lipid Membranes at Bifaces
where the subscripts to the y's refer to the various liquid phases. At equilibrium, the theorem of Neumann's triangle states (13) that the magnitude of
each of three interfacial tensions is proportional to the sine of the angle between the other two interfaces,
_
I-III
_
'YBLM
sin ( -
sin (a + 8
3)
I-III
(
sin (r -a)
)
Normally, the two aqueous phases I and II are identical. Therefore, YI-m
equals YII-III, and a = 1 = 0. From elementary trigonometry, it can be
shown that
7BLM =
2
(4 )
ML COS 0
.
=
2ML COS a +
( 5)
YR
where on the right-hand side the first term is the vertical component of the
interfacial tension and the second represents the P-G border suction pressure.
The horizontal distance, S, is given by
(6)
S = 2R ( - cos a)
The observable circular area of BLM is governed by
'YBLM,
YML,
and the
angle 0. If 0 is zero, then, upon substitution of S into equation 5, we have
TBLM
=
2YML
(
7)
In that case no BLM is obtainable. If 0 is greater than zero, the distance S is
S = 2R (cos0 - cos ca)
which means that
7yBLM
must be less than
2
(8)
yML . In order for this to be true,
the P-G border must move toward the rim of the aperture as dictated by
equation 4. The latter situation is shown by the dashed line in Fig. 3 B.
The ideas discussed here may be further developed to provide an alternative
means of evaluating the tension of the BLM.
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where ML denotes the interfacial tension between two bulk phases in the
presence of a lipid monolayer. At the P-G border, the interfaces are circular
according to the Young-Laplace equation, with radius equal to R. At equilibrium, the downward tension (YBLM) must be balanced by the upward tension
y,, which may be split into two terms, and given by
Published July 1, 1968
132 s
MODELS
OPTICS AND
OF BLM
STRUCTURAL
AND
MODEL
MEMBRANES
ASPECTS
As mentioned in the preceding paragraphs, BLM are formed in aqueous
solution by a process similar to the generation of black soap films in air.
The optics of BLM are essentially those of very thin films. (According to the
definitions used in thin film optics, a thin film is a layer with parallel faces
whose thickness, t, is of the order of the wavelength, X, of light used. A very
thin film has t less than 0.01X.) The common optical measurement thus far
made on BLM is the reflectance at a small angle of incidence using visible
electromagnetic radiation. The results are interpreted in terms of either a
homogeneous structure (single-layer model) or a triple-layer model. In the
TABLE II
BLM from
Solvent
Aqueous phase
Thickness*
Reference
A
0.1 N NaCI
694-10
77410t
72-10
15
15
17
?
Various
0.1 N NaCL
0.1 N NaC
744-15
5045
4010
404-10
18
8
8
8
Lecithin
n-Decane
0.1 N NaC
Lecithin
CHCI 3 + CHSOH + n-tetradecane
?
n-Hexane
n-Octane
C6-C 1 4
Phospholipids (?)
Glycerol distearate
Oxidized cholesterol
7-Dehydrocholesterol
*
Unless otherwise noted, the thickness values were calculated using equation (9).
Calculated using equation 10.
latter model, the polar (or ionic) portions of the lipid molecules situated at the
biface form the two outer layers with a liquid hydrocarbon core in the center.
To evaluate the thickness of BLM from reflectance measurements, the following equations are used:
Rs
4r2 sin2 S
(1 -- r ) + (2r sin =)2
2 2
(9)
for the single-layer model, and
R =
=
rl2
+ 72 + 2rxr' cos (X1 - h)
I + r 2 " 2 + 2rxr" cos (xi - ah)
(10)
for the triple-layer model. In equations 9 and 10, r's are the various Fresnel
reflection coefficients,
= (27rnbtb cos O)/X, in which t is the thickness, 0 (or
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THICKNESS OF BIOMOLECULAR LIPID MEMBRANES AS
DEDUCED FROM OPTICAL MEASUREMENTS
Published July 1, 1968
H. T TIEN Black Lipid Membranes at Bifaces
133 s
h) is the reflected angle in the membrane, n is the membrane refractive
index, and X is the wavelength of the visible radiation used (see, for example,
reference 14). In applying equation 9, one has to assume or know the value of
the membrane refractive index, nb . For a homogeneous and isotropic structure
of BLM, Brewster's law (tan ), = nb/n.) may be used to estimate the index
of the membrane. It is based upon the property that for light polarized with
the electric vector in the plane of incidence, the reflectance of a transparent
film of refractive index nb immersed in a medium of index n, is minimum at
the polarizing angle 4p,. The thickness values obtained using equation 9 are
shown in Table II, and lend support to the contention that BLM consists of a
bimolecular layer of lipid held together by van der Waals' forces. The large
error (approximately 10%) in the results is due mainly to the uncertainty in
X1 -
Triple-layer model
p
[1]
[2]
ah = 1.44
[3]
n = 1.46
[4]
Single-layer model
n = 1.56
[5]
t
[6]
5.129
6.208
7.388
8.671
10.056
7.477
8.769
10.162
11.658
13.255
10.309
11.816
13.425
15.136
16.948
32.325
34.949
37.675
40.500
43.426
50
54
56
58
60
nA
1.42
A
A
1
2
3
4
5
the Brewster's angle determination. Furthermore, there is some question concerning the applicability of Brewster's law to the determination of the refractive indices of very thin films such as BLM. This difficulty in assessing refractive index of the membrane using Brewster's law may be avoided, however, if
we assume that the index of refraction of the BLM varies little with wavelength of light used. We are currently experimenting with this approach, and
the steps are outlined below.
It is evident from equation 9 that two equations are required to determine
the two quantities nb and tb. Experimentally, one needs to measure Rt as a
function of wavelength X, as has been suggested by Abelas (14). The quantities
dependent on the wavelengths XI and X2 are designated by the subscripts 1 and
2 and
Al
= I + R.
- R(1
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TABLE III
CALCULATION OF THE REFLECTANCE (R X 105) FOR DIFFERENT
VALUES OF nh AS A FUNCTION OF t,
Other values used: n,, = 1.33; n, = 1.56; t = 48; X = 4350.
Published July 1, 1968
134 s
MODELS AND MODEL MEM73RANES
A2 =
(12)
I -R2
1 - Rt2
The optical thickness of the membrane is given by the equation
(2n,2 - 2A 2n,o2) cos
1 - (2n,2 - 2Ain 2 ) cos 62 = 2n, 2 (A1 - A)
(13)
Since 2 = (X1/X2 ) l1, the only unknown in equation 13 is 61, which can be
readily evaluated from experimental data. The refractive index nb of the
membrane may be found using the following equation:
nb4 [(2n, 2)(1 +
cos 1) - 4n 2A 1 n
2+
4
(14)
=
TABLE IV
Triple-layer model
1p
[1]
nAh
1.
56
[2]
nh
1.53
[3]
nh =
1.60
[41
Single-layers model
6
nh
1. 3
t
[5]
[6]
A
2
6
8
10
14
A
3.959
5.623
6.561
7.571
9.801
4.660
6.452
7.454
8.527
10.883
5.428
7.348
8.451
9.552
12.036
6.707
8.824
9.988
11.222
13.899
54
62
66
70
78
It remains to be seen whether this method, due to Abeles (14), can provide us
with more information concerning the detailed structure of BLM.
The considerations presented above are based upon the supposition that the
structure of BLM is homogeneous and isotropic. However it has been proposed
that a BLM is not likely to be a homogeneous and an isotropic structure. This
stems from the fact that the compounds so far established for BLM formation
are all amphipathic in nature. Hence, a more realistic model consisting of
three layers is proposed for the BLM (15). The detils will not be repeated
here. The following paragraph is concerned with the results of further computation using equation 10, and points out their significance in relation to
the structure of BLM.
As mentioned above, the quantity most accessible to direct experimental
measurement is the reflectance of the membrane. Calculations are therefore
carried out for the reflectance, Rt, using equation 10. The calculations are
made for varying thicknesses, t, of the polar (or ionic) layer and refractive
indices. The wavelength of the incident light is 4350 A. The thickness of the
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CALCULATION OF THE REFLECTANCE (R X 104) FOR DIFFERENT
VALUES OF nh AS A FUNCTION OF t,
Other values used: n
1.33; n = 1.63; th = 50; X = 4350.
Published July 1, 1968
H. TI TIEN
Black Lipid Membranes at Bifaces
135
central hydrocarbon region is assumed to be either 48 or 50 A. The results for
two typical cases are shown in Tables III and IV. In both tables, columns
2-4 give the reflectances of BLM according to the triple-layer model. Columns
5 show the reflectances of membranes having a homogeneous single-layer
structure. The last column of each table presents the over-all thicknesses of
the BLM using t = 2t, + th. It is evident from the results of calculations that
the reflectances of BLM are very sensitive to the polar group thickness and
membrane refractive index used, with the latter having a much greater effect
Arrangement of ap-
paratus used for measuring the
interfacial tension of bimolecular linid membranes.
Infusion- Withdrawal
Pump
than the former. The results presented in these tables are useful in that they
may be employed to check the experimentally measured reflectance values.
The relationship between the single-layer and triple-layer models has been
discussed in an earlier publication (15). In general, the thickness is about
10% lower as calculated according to Rayleigh's equation.
METHOD OF MEASURING
BY BULGING
BLM
TENSION
Since the classical techniques for measuring the tension of films at interfaces
(oil/water or air/water) are not easily extended to BLM, a novel method has
been developed using highly sensitive pressure transducers which have become
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FIGURE 4.
Published July 1, 1968
136 s
MODELS AND
MODEL MEMBRANES
pH
AND
SALT
EFFECTS
ON
yi
Although no systematic studies of pH and salt effects on the interfacial tension
of BLM have been carried out, the following tentative conclusions may be
drawn from a few scattered experimental observations. (a) For BLM generated from lipids bearing ionizable groups, the yi values are lower than for
BLM containing anionic lipids at higher pH's. The opposite may be said to
hold for BLM with cationic lipids (b) For BLM formed from neutral lipids,
pH has only secondary effects on yi This is also true for changing salt concentrations. However, a much more noticeable salt effect is observed for
BLM produced from lipids with charged groups. For example, the interfacial
tensions of BLM formed from cholesterol-HDTAB-dodecane in water and in
0.1 N NaCl are, respectively, 0.15 and 0.65 dyne/cm. Similarly, the dioctadecyl phosphite membrane in water has a yi value of 5.7 dynes/cm as compared with 3.9 dynes/cm when measured in 0.1 N NaCl.
To sum up the observations on the y's of the BLM generated from a num-
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recently available (Sanborn model-270 and Pace model P-90D have been
used). The theory on which the "bulging" method of measuring BLM tension
is based is very simple. It is essentially a modification of the so-called maximum bubble pressure method (16). In applying the method to BLM systems,
it is assumed that the conventional definition of interfacial tension is valid.
The other assumptions are that equilibrium conditions exist and the BLM
support is completely wetted by the lipid solution. Experimentally, a BLM is
first formed at the biface. The hydrostatic pressure is then applied by slowly
infusing a solution to one side of the membrane. The pressure difference, P,
across the BLM is continuously recorded and reaches a maximum when the
BLM is bulged into a hemisphere. The tension of the BLM is calculated at
this point using the relation y = Pd/8, where a is the diameter of the opening.
Fig. 4 illustrates diagrammatically one type of experimental arrangement used
in the determination of interfacial tension of the BLM at the biface. The
calculated results, together with the composition of BLM forming solutions
are given in Table I.
It should be pointed out that the bulging method is not only useful for
BLM systems at W/O/W bifaces but suitable also for other situations where
two bulk phases are being separated by a thin layer (soap films, monolayers,
multilayers, or immiscible liquids). Certain advantages of this method may be
stated: (a) only a small quantity of test liquid is necessary; (b) temperature
control is easy; (c) interfaces (or biface) can be easily renewed, thus reducing
contamination. It seems that at the biface the only "mechanical" property
which is directly measurable is the interfacial tension. Therefore, the method
should also be of value in studying the interactions of drugs, proteins, and
other agents with BLM.
Published July 1, 1968
H. TI TIEN
Black Lipid Membranes at Bifaces
137
ber of compounds, the results strongly suggest that a low y value is a prerequisite for stable BLM formation; the lower limit is slightly above zero.
The upper limit of the y value, if it exists, cannot exceed about 9 dynes/cm.
THE THERMODYNAMICS
AT THE BIFACE
OF
BLM
P = Pi - t
(15)
_
Therefore, the pV work for the interfacial layer is equal to
PVBLM -
( 16 )
A
where VBLM = t'A, and A is the area of the membrane. For the BLM, the
general variation of the Helmholtz free energy is given by
dFBLM = -SLM dT - p dVBLM +
dA + E
dn
( 17 )
where ,Aand n are the chemical potential and the number of moles in each
phase, respectively. By manipulating these equations in the customary manner, we can obtain the Gibbs-Duhem equation for BLM, i.e.
SBLM dT - VBLM d + A dy +-
n du = O
( 18 )
If equation 18 is divided throughout by A, it becomes
SBM dT - t dp + dy +
r du = O
(19)
where SLM is the entropy per unit area of BLM, and r is the so-called interfacial excess. It is evident that equation 19 is a form of the Gibbs adsorption
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In this section the classical thermodynamic equations of the interface between
two bulk phases developed by Gibbs will be applied to the BLM system (19).
We shall assume that each extensive property of the system, such as the free
energy F, the entropy S., or the number of moles of each component, is the
sum of three parts: (a) the contribution of aqueous phase I, (b) the similar
contribution of aqueous phase II, and (c) the BLM, which has a small but
definite uniform thickness. This is consistent with the usual picture of two
homogeneous aqueous solutions between which a BLM is interposed. Since
BLM has a "well-defined" structure, we may speak of its temperature T,
free energy, etc., just as for the two aqueous phases I and II. The exceptions
to these quantities are the pressure and interfacial tension. In the case of
pressure, the force per unit area exerted perpendicularly on the BLM is
Published July 1, 1968
138 s
MODELS
AND MODEL
MEMBRANES
equation, which will be considered further in connection with the BLM
structure. We can also write the change of y with temperature, which is
given by
-d = SBLM-td
+
r dp
(20)
(a74 = - (dAT
(a
(21)
\dT~a-
Since dq = Tds, where q is the quantity of heat involved, it follows also that
(d
)
=
(22)
T (z)'
according to the laws of thermodynamics. The total internal energy of the
BLM for a unit area (1 cm 2 ) increase is then the sum of two quantities; i.e.
EBLM
=
'YBLM
T
--
(23)
The first term on the right side of equation 23 is the so-called free energy of
the membrane. The quantity T(ay/o T)A is the amount of energy which
must be supplied from the bathing solution. Rigorously speaking, the second
term on the right-hand side of equation 23 is not to be neglected. However, in
using the y = Pd/8 relation, it has been assumed that the process is carried
out isothermally with that portion of the energy provided by the surrounding
medium.
THERMODYNAMICS
OF BLM
FORMATION
The formation of a BLM at a biface may be imagined to take place in three
experimentally distinguishable steps. These are (a) the creation of a water/oil/
water (or W/O/W) biface, (b) the adsorption or migration of interfacially
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We shall now attempt to apply these equations to the BLM system. Before
doing so, it seems appropriate to recall the behavior of molecules at oil/water
interfaces and their relation to the bifaces. Generally speaking, relatively high
tensions are observed at the bulk oil/water interfaces (about 50 dynes/cm for
long-chain hydrocarbon vs. H 2 0O). By introducing polar (or ionic) groups
into the hydrocarbon molecules, the y can be greatly lowered. When a BLM
is extended, the external work done on the membrane is y dA. If the process
is carried out isothermally and at constant pressure and composition, we can
define, in the conventional manner, the entropy of BLM formation as -dy/
d T. Recalling that dF is a perfect differential of F (the Helmholtz free energy)
with respect to the two variables, T and A, we obtain
Published July 1, 1968
H. Ti
TIEN
Black Lipid Membranes at Bifaces
I39
active molecules to the biface, and (c) the formation of the BLM from the
monolayers situated at the biface. These individual steps, together with the
accompanying free energy changes, are given by the following equations:
Liquid hydrocarbon (0) + H20 (W) - W/O/W + AF 1
(24 )
W/O/W + lipid -- monolayers (ML) + AF2
(25 )
ML -- bilayer lipid membrane (BLM) + AFs
(26)
It is evident that the over-all reaction is
Liquid hydrocarbon + H20 + lipid -- BLM + AFi
(27)
AF2
=
AF3 =
ML YBLM -
AFi = YBLM -
'O/W
(28)
YML
(29)
VO/W
(30)
where yo/w is the interfacial tension of the oil/water interface, and 'ML and
YBLM are, respectively, the interfacial tension of the monolayer and the BLM.
As a specific example, the experimental data are available for BLM formed
72, yo - 22 (n-dodecane), 'Yo/w
50,
from lecithin-dodecane system: yw
YML
6.5, and YBLM - 0.9. Thus, the free energy change in the formation of
BLM from lecithin at a clean W/O/W biface is about 50 ergs/cm2. Assuming
the area occupied per lecithin molecule in the BLM to be 50 A 2, the molar
free energy change is calculated to be 3.6 kcal.
It is seen that the formation of BLM at bifaces is akin to the process of
spreading monolayers at air/water or oil/water interfaces. With suitable
lipid solutions, such as oxidized cholesterol in octane, a BLM is formed
spontaneously. That is, when a drop of lipid solution is introduced into the
aperture, it never forms a stable thick membrane, but the drop thins down
rapidly to the P-G border in equilibrium with a BLM. Since yBLM for the
membrane is very small (usually less than 6 dynes/cm), the molecules in the
membrane must be under very high compression. The resulting structure
(BLM) has a close-packed arrangement which is thought to be not unlike
'
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where AFi is the sum of three free energies. In equations 25 and 26, it is
understood that both the monolayers and the BLM are in equilibrium with
the Plateau-Gibbs border. From surface film studies, it is generally known
that the tendency for a liquid hydrocarbon (e.g. n-dodecane) to spread on a
clean water surface is nil, owing to the negative spreading coefficient. Therefore, AF1 is approximately equal to zero. Expressing other AF's in terms of
interfacial tension (free energy), we have
Published July 1, 1968
14o s
MODELS AND MODEL MEMBRANES
APPLICATION
EQUATION
OF GIBBS'
TO BLM
ADSORPTION
SYSTEM
As mentioned in the section on the P-G border and BLM stability, one of the
major problems is that we do not have any precise knowledge concerning the
chemical composition of the membrane. The need for such knowledge is
evident, since any quantitative considerations of BLM would have proceeded
more rapidly had we possessed such information. At present, the use of direct
chemical analysis for BLM composition is not feasible owing to the very small
areas and thickness of the membrane (8). One way to approach this problem
would be to resort to the use of Gibbs' adsorption isotherm given earlier
(equation 19). The use of equation 19 might be possible if the quantity y is
identified with the YBLM ·. In order to calculate the excess concentration of
lipid molecules in the BLM, the usual extrathermodynamic assumption would
also have to be made in that the only species in the membrane would be the
surface-active lipid molecules. Since the Gibbs equation relates the YBLM and
the concentration of the dissolved material, therefore, a knowledge of the
interfacial concentration of adsorbed molecules would permit an evaluation
of the area occupied by BLM-forming molecules. From this information
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that of liquid crystals in two dimensions. Further discussion of the BLM
structure will be given in the section on the Gibbs adsorption isotherm.
Using BLM generated from dodecyl acid phosphate-cholesterol-dodecane
in 0.1 N NaCI as illustrated, the temperature variations of the y's have been
determined. From equations presented above and the experimental data, the
entropy, free energy, and enthalpy of BLM formation may be calculated.
The results show that the free energy of formation of BLM decreases slightly
with increasing temperature for the temperature range investigated (2544.5 0 C). This slight decrease is consistent with the idea that the major portion
of the work involved is the formation of a duplex film (using Harkins' terminology) at the biface. At higher temperatures, the concentration of adsorbed
lipid molecules will be less. Hence a lower free energy should result. The
entropies of formation are all negative, ranging from 0.008 at 250 C to 0.264
erg/cm2-deg at 44C. This means that the latent heats of formation are also
negative. Therefore, in the process of formation of BLM, an evolution of heat
takes place, which is also accompanied by a decrease in entropy. One obvious
explanation is the changes in the orderliness of constituent molecules at the
biface. As would be expected, the lipid molecules possess a higher degree of
order in the BLM state than in the lipid solution. The larger decrease of
entropy at a higher temperature seems to imply that a change has taken place
in the monolayer structure, whereas the organization of the BLM is not much
affected by a moderate rise in temperature. Similarly, much the same argument may be used to explain the negative enthalpy of formation data.
Published July 1, 1968
H. T TIEN
Black Lipid Membranes at Bifaces
14I s
certain deductions concerning the structural aspects of the membrane might
be made. We now present results of an investigation of BLM generated from
the cholesterol-dodecane-HDTAB (hexadecyltrimethylammonium bromide)
system as a specific example.
With the aforementioned assumptions in mind, equation 19 may be written3
as
-dBLM
=
RT rc d In [C] + RT r, d In [HDTAB]
(31 )
TABLE V
INTERFACIAL CONCENTRATION EXCESS AND MINIMUM
AREA OCCUPIED BY THE ABSORBED SPECIES
FROM INTERFACIAL TENSION DATA AT 25°C
System
HDTAB-C 1 2 -H2 0
HDTAB-cholesterol-C12-H20*
Cholesterol-C12-H20
*
Concenration excess
Area
mole/ca2
A/moleeule
2.1X 10 - 0
7 .8X 10-11
-1 0
5.6X10
80
200
30
Stable BLM obtained with this system only.
one would like to obtain the y vs. concentration plot for one component while
holding the concentration of the other constant. However, we have not been
able to produce BLM from either cholesterol or HDTAB alone, and so the
data even for this simple BLM system are not complete. Therefore, the discussion which follows is presented to show that structural information may be
obtained in spite of the limited data. It should be mentioned that the values
for the area occupied per molecule given in Table V are expressed in terms of
minimum area because of the lack of activity coefficient data and drastic
simplifications used in the application of Gibbs' equation. In the case of
HDTAB in the presence of cholesterol, the area is found to be about 200 A2 .
This value is calculated from the slope of yBLM vs. [HDTAB] in the aqueous
phase at a constant concentration of cholesterol. If we assume that the area
occupied by the respective species remains unchanged in the membrane, this
a For simplicity, we have used the concentrations instead of activities. Also, for the dissociable surfactant, HDTAB, a factor of 2 should be taken into consideration.
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under constant temperature and pressure conditions, where r and r H refer
to the interfacial excess concentrations of cholesterol and HDTAB, respectively. The respective interfacial excess may be obtained from the slope of
y vs. concentration plots in the usual manner. In the present study, all y
measurements were made at the biface using the bulging method (Fig. 4).
The calculated results are given in Table V. It should be stated that ideally
Published July 1, 1968
I42 s
MODELS
AND MODEL
MEMBRANES
would mean that the molar ratio of the cholesterol to that of HDTAB is about
3: 1 in the BLM. To account for this particular ratio, a most likely arrangement would be that of a hexagonal packing with 6 cholesterol molecules
around each HDTAB. It is argued that the slenderness of the HDTAB hydrocarbon tail could easily fit into the space between the cholesterol molecules,
with the head group of HDTAB sticking out at the membrane/solution interface. A probable structure of BLM produced from cholesterol-HDTAB as
deduced from the above data is illustrated diagrammatically in Fig. 5. It
seems likely that the insertion of HDTAB into the cholesterol "bilayer leaflet"
may account for the BLM stability.
(B)
CONCLUSIONS
BLM, a unique type of interfacial membrane, has been shown to be an important tool for the investigation of membrane phenomena in relation to
biological membranes (8). Thus far, certain semblances have been demonstrated between natural membranes and BLM. However, we are still ignorant
about the exact composition and structure of these membranes. The study of
unmodified BLM, though important in its own right, cannot hope to elucidate
the basic functions and structural aspects of natural membranes. Nevertheless,
the fact that today we are able to manipulate a structure of molecular dimension, and, most of all, that such a delicate structure can be formed in vitro
between two aqueous solutions, offers a wide variety of opportunities for its
modification. These could then be used for studies such as membrane transport, conductivities, and membrane potentials. The important feature of the
BLM lies in the possibility that BLM, when constituted from appropriate
compounds, may be used as "model systems" in the understanding of visual
process, and photosynthesis and related phenomena in which lamellar structures are known to be important. It is hoped that a detailed physical chemical
description of the BLM system would be useful in providing a more rational
basis for further development.
This work was supported by Public Health Service grant GM 14971 from the National Institutes of
Health.
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(A)
FIGURE 5. BLM produced from the cholesterol-HDTAB system. A. A front view of a
sheet of cholesterol molecules at the water/oil/water biface. B. Adsorption of hexadecyltrimethylammonium bromide (HDTAB) stabilized the system, leading to BLM formation. Open circles, cholesterol; larger circles with hatched centers, HDTAB.
Published July 1, 1968
H. TI TIEN
Black Lipid Membranes at Bifaces
I43
REFERENCES
18. BABAKov, A. V., L. N. ERMIsHKIN and E. A. LIBERMAN. 1966. Influence of electrical field
on the capacity of phospholipid membranes. Nature. 210:953.
19. GUGGENHEIM, E. A. 1950. Thermodynamics, North Holland Publishing Company, Amsterdam. 220.
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1. DAVSON, H. 1962. Growth of the concept of the paucimolecular membrane. Circulation
26:1022.
2. GORTER, E., and R. GRENDEL. 1925. On bimolecular layers of lipoid on the chromocytes of
the blood. J. Exptl. Med. 41:439.
3. HARVEY, E., and H. SHAPIRO. 1934. The interfacial tension between oil and protoplasm
within living cells. J. Cellular Comp. Physiol. 5:255.
4. COLE, K. S. 1932. Surface forces of the Arbacia egg. J. CellularComp. Physiol. 1:1.
5. FISHMAN, A. P. (editor). 1962. Symposium on the Plasma Membrane. Circulation. 24(2, Pt.
2) :983.
6. MUELLER, P., D. O. RUDIN, H. T. TIEN, and W. C. WEcorr. 1962. Reconstitution of cell
membrane structure in vitro and its transformation into an excitable system. Nature. 194:
979.
7. MUELLER, P., D. O. RUDIN, H. T. TIEN, and W. C. WEscorr. 1964. Formation and properties of bimolecular lipid membranes. In Recent Progress in Surface Science. K. G. A.
Pankhurst and A. C. Riddiford, editors. Academic Press, New York. 379.
8. TIEN, H. T., and A. L. DIANA. 1968. Bimolecular lipid membranes: a review and a summary of some recent studies. Chem. Phys. Lipids. 2:55.
9. LAWRENCE, A. S. C. 1929. Soap Films. G. Bell & Sons, Ltd. London.
10. OVERBEEK, J. T. G. 1960. Black soap films. J. Phys. Chem. 64:1178.
11. Duyvis, E. M. 1962. The equilibrium thickness of free liquid films. Doctorate Thesis.
Utrecht. 31.
12. PRINCEN, H. M., and S. G. MASON. 1965. Shape of a fluid drop at a fluid-liquid interface. J.
Colloid Sci. 20:156.
13. ADAM. N. K. 1941. The Physics and Chemistry of Surfaces. Oxford University Press, London. 209.
14. ABELS, F. 1950. The determination of the index and thickness of transparent thin films.
J. Phys. Radium. 11:310.
15. TIEN, H. T. 1967. Black lipid membranes: thickness determination and molecular organization by optical methods. J. Theoret. Biol. 16:97.
16. ADAMSON, A. W. 1967. Physical Chemistry of Surfaces. John Wiley & Sons, Inc., New York.
2nd edition. 18.
17. HuANo, C., T. THOMPSON. 1966. Thickness of bilayer membranes. J. Mol. Biol. 16:576.
Published July 1, 1968
144s
MODELS AND MODEL MEMBRANES
Discussion
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Dr. Mysels: I wonder whether, Dr. Tien, in going to the surface area from the
measurement of surface tension changes upon addition of quaternary ammonium
salt, we don't have to make some assumption about the constancy of absorption of the
cholesterol or something of that sort?
Dr. Tien: Yes. For a two-component system, the ideal situation is to measure interfacial tension change with respect to the concentration of one substance and holding
the other one constant. You do the same thing for the other component. In this way
you can obtain the sum of the two interfacial excesses.
Does that answer your question, Dr. Mysels?
Dr. Mysels: Yes.
Dr. Miller: I am not sure that I really understood every stage of the discussion because I couldn't see the tables very well, but I was wondering about the interpretation of the stability of the bilayer. If I did understand, it was based on consideration
of the interfacial tensions. Am I correct?
Dr. Tien: Not quite. I think that a low value of interfacial tension is one of the prerequisites for the formation of a stable black lipid membrane.
Dr. Miller: What I really mean is the difference between the interfacial tension
of the bilayer water interface and the oil/water interface, AF. Is this AF related to
some equilibrium phenomenon, or is it related to some transient process? That is,
during the burst or destruction of the bilayer you create transiently an oil water
interface by investment of the energy AF, which in this case would become a component of an activation energy. Besides that, shouldn't some structural contributions
and cohesion forces also be considered?
Dr. Tien: The interfacial free energy (or tension) to which I was referring is the
free energy of formation measured at equilibrium conditions; that is, the energy required to form a black lipid membrane at the biface (i.e. the two coexisting water/oil
or solution/membrane interfaces) from initially cleanwater/oil interfaces. With regard
to the latter part of your comments, I can only say that the process leading to black
lipid membrane formation is not very well understood at the present. Perhaps the
question you posed and certain aspects I discussed in my paper will stimulate some
interest in that direction.
Dr. Mauro: Would you care to speculate on your extensive investigations on lipid
molecules? What would be the minimal length of the lipid chain that would give you a
so-called secondary film?
Dr. Tien: In reply to your question, Dr. Mauro, I would like to say that a chain
length of about 12 carbon atoms seems to be necessary (see Table I of my paper).
This is based upon the fact that we have been able to produce black membranes
stabilized by esters of lauryl alcohol. Perhaps Clo or even lower hydrocarbon chain
lengths are also possible, but I do not have any definite information.